Question

if the polynomials az^3+4z^2+3z-4 and z^3-4a+a leave the same remainder when divided by z-3 find the value of a

Answer 1

$f(z) = a {z}^{3} + 4 {z}^{2} + 3z - 4 \\ p(z) = {z}^{3} - 4a + a \\ same \: remainder \: when \: divided \: by \: z - 3 \: then \: find \: the \: value \: of \: a$
$from \: question \: f(z)= p(z) \\ 27a + 36 + 9 - 4 = 27 - 4a + a \\ 30a + 41 = 27 \\ 30a = 27 - 41 \\ 30a = - 14 \\ a = - 14 \div 30 \\ a = - 7 \div 15$
hope it helps you